High Dimensional Data Analysis: Overview, Analysis, and Applications

A data mining and feature extraction technique called Signal Fraction Analysis (SFA) is introduced. The method is applicable to high dimensional data. The row-energy and column-energy optimization problems for signal-to-signal ratios are investigated. A generalized singular value problem is presented. This setting is distinguished from the Singular Value Decomposition (SVD). Two new generalized SVD type problems for computing subspace representations is introduced. A connection between SFA and Canonical Correlation Analysis is maintained. We implement and investigate a nonlinear extension to SFA based on a kernel method, i. e., Kernel SFA. We include a detailed derivation of the methodology using kernel principal component analysis as a prototype. These methods are compared using toy examples and the benefits of KSFA are illustrated. The book studies the applications of the proposed techniques in the brain EEG data analysis and beam-forming in wireless communication systems.